Wifi and Bluetooth are used for 2 completely different uses.
It is rare to use Bluetooth for WLAN (wireless local area network) and Internet Access (with the exception of cell phone tethering)
Yes Bluetooth (IEEE 802.15.1) is technically older, Ericsson came up with bluetooth in 1994. Bluetooth uses a short-range radio frequency band for ad-hoc network connections with peripheral devices (head sets, game pads, Keyboard, mouse, printers, medical devices, GPS devices ect). Bluetooth is often used when low bandwidth applications where higher USB bandwidth is not required and cable-free connection desired.
Bluetooth is far from outdated, Wii Remotes, PS3 Dual Shock Controllers and wireless cellphone headsets are examples of prime Bluetooth territory.
Wi-Fi (IEEE 802.11) came out in 1999 (not that far off from Bluetooth). Wifi has several revisions, most common are A,B,G and N.
Wi-Fi is purely used for WLAN applications. Yes Wi-fi has further range, but this is a moot point for local multiplayer.
For a local 1 on 1 Street Fighter match on iOS, you are perfectly fine on Bluetooth.
Over Wi-fi you are tiding up some of your wireless router’s bandwidth for your game (not all devices or games support Wi-Fi ad-hoc mode), poetically hurting anyone else on the WLAN network who might need network or internet access.
Alots of use or heavy network traffic can effect your Wi-Fi multiplayer game with lag. Example your little sister with the 27 MP3 torrents, your brother playing World of WarCraft while mom and dad in the living room watching Netflix on their TV will all effect your Wifi connection.
Bluetooth does not require a router, and the odds you have a interfering signal is unlikely.
The Rest of your house hold will not effect your game play by heavy network use.
sources for this information can be found on Wikipedia.